In game-theoretic statistics we have some wealth process where the “payoffs” are e-values depending on some predictable “bet” . The e-values might be of exponential form (see exponential inequalities) or of the form (eg estimating means by betting).
We want to increase if some null is not true. If a particular alternative is known, we might consider designing the according to some growth rate conditions in sequential testing. If not, we need to do something else. Here we gather various strategies.